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The main objective of this work is to estimate, semi-parametrically, the mode of a conditional density when the response is a real valued random variable subject to censored phenomenon and the predictor takes values in a semi-metric space. We assume that the explanatory and the response variables are linked through a single-index structure. First, we introduce a type of kernel estimator of the conditional density function when the data are supposed to be selected from an underlying stationary and ergodic process with missing at random (MAR). Under some general conditions, both the uniform almost-complete consistencies with convergence rates of the model are established. Further, the asymptotic normality of the considered model is given. As an application, the asymptotic (1−α) confidence interval of the conditional density function and the conditional mode are also presented for 0 < α < 1.

The main objective of this paper is to investigate the estimation of conditional density function based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. As an application the conditional mode in functional single-index model is presented. Finally, a simulation study is carried out to evaluate the performance of this estimate.

In this paper, we study an kernel estimator of the conditional hazard quantile function (CHQF) of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space and using the proposed estimator based of the kernel smoothing method. The almost complete consistency and the asymptotic normality of this estimate are obtained when the sample is an independante sequence.

We consider the problem of nonparametric estimation of the conditional hazard function for functional mixing data. More precisely, given a strictly stationary random variables Zi = (Xi; Yi)i2N, we investigate a kernel estimate of the conditional hazard function of univariate response variable Yi given the functional variable Xi. The principal aim of this paper is to give the mean squared convergence rate and to prove the asymptotic normality of the proposed estimator.